ap precalc unit 7 test

pythagorean identities (sin and cos)

sin²x+cos²x=1

pythagorean identities (tan and sec)

1+tan²x=sec²x

pythagorean identities (cot and csc)

1+cot²x=csc²x

tanx quotient identity

tanx=sinx/cosx

cotx quotient identity

cotx=cosx/sinx

sin(-x)

-sinx

cos (-x)

cosx

tan (-x)

-tanx

csc(-x)

-cscx

sec(-x)

secx

cot(-x)

-cotx

sin (a+b)

(sina)(cosb)+(cosa)(sinb)

sin(a-b)

(sina)(cosb)-(cosa)(sinb)

cos(a+b)

(cosa)(cosb)-(sina)(sinb)

cos(a-b)

(cosa)(cosb)+(sina)(sinb)

tan (a+b)

tan a +tan b/1-(tan a)(tan b)

tan (a-b)

tan a-tan b/1+(tan a)(tan b)

sin (2x)

2sinxcosx

cos (2x)

cos²x-sin²x

tan (2x)

2tanx/1-tan²x

slope of terminal ray of an angle

tangent function

all real numbers, x does not equal to pie over two + pie k

domain of tan

all real numbers

range of tan

pie

period of tan

[-1,1]

domain of arcsinx

[-pie/2, pie/2]

range of arcsinx

[-1,1]

domain of arccosx

[0,pie]

range of arccosx

(-infinity,infinity)

domain of arctanx

(-pie/2, pie/2)

range of arctanx

(-infinity, -1] U [1, infinity)

range of cscx

(-infinity, -1] U [1, infinity)

range of secx

(-infinity, infinity)

range of cotx

0, pie, 2pie

asymptote of cscx

pie/2, 3pie/2, 5pie/2

asymptote of secx

0, pie, 2pie

asymptote of cotx

x=rcostheta y=rsintheta

polar to cartesian

r = root x²+y² theta= tan^-1 (y/x)

cartesian to polar

n petals/2n petals

n is odd/n is even

2pi/# of petals

distance between petals

pie/2n

1st petal sin

z=a+bi

(a,b)

z=r(costheta+sinttheta)

(r, theta)

a/b=1

cardoid

1<a/b<2

dimpled cardoid

a/b<1

limacon